The Gunners had defender Rob Holding sent off in the first half and Arteta was angered that his team's hopes were dashed by the match officials.
He told Sky Sports: "If I say what I think I am suspended for six months. I don't know how to lie so I prefer not to say what I think. I cannot say what I think.
"I want the referees to come in front of the camera and explain his decisions. It's a shame because such a beautiful game was destroyed today.
"I am not unhappy with my players. I am proud of my players. The decision was made. We can't change it. The referee has to make a decision in football."
Arsenal now need to win their last two matches to secure Champions League qualification and Arteta is keen to move on from the derby loss.
He said: "Our focus is Newcastle. This game is history. This is gone. It went out of our hands and we have to accept it. Now we need to be the team that you saw from the beginning.
"When you lose a football match in the conditions we lost them, it's painful. But we have a huge match on Monday so we will try to beat them. We have two games to play each. It's in our hands and now we have to do our jobs. We showed from the beginning in this game."